Question: Rewrite as a simplified fraction. ${1.62\overline{3} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1623.3333...\\ 100x &= 162.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1461}$ ${x = \dfrac{1461}{900}} $ ${x = \dfrac{487}{300}} \text{or} {1 \dfrac{187}{300}}$